
The extended Hessian at \((B_0,\Psi _0)\)  [1]} is then the operator on \(i\Omega ^0\oplus T\mathcal {C}\)  given in block matrix form as
\(\widehat{\mathrm {Hess}}\mathcal {L}_{(B_0,\Psi _0)}=\begin{bmatrix}0 & \mathbf {d}_{(B_0,\Psi _0)}^* \\\mathbf {d}_{(B_0,\Psi _0)} & \mathrm {Hess}\mathcal {L}_{(B_0,\Psi _0)}\end{bmatrix};\) 
